Eigenmodes of a disordered FeCo magnonic crystal at finite temperatures

TL;DR

This study compares two computational approaches to analyze magnonic modes in a disordered FeCo alloy, revealing that the CPA effectively predicts energies but underestimates damping due to non-local effects, and explores temperature effects on eigenmodes.

Contribution

It systematically compares the real-space averaging and CPA methods for disordered magnonic systems, highlighting the strengths and limitations of CPA in predicting magnon properties.

Findings

CPA accurately predicts magnon energies and eigenmode shapes

CPA underestimates disorder-induced magnon damping

Temperature influences eigenmode spatial shapes

Abstract

In this report we present a systematic study of the magnonic modes in the disordered Fe$_{0.5}$Co$_{0.5}$ alloy based on the Heisenberg Hamiltonian using two complementary approaches. In order to account for substitutional disorder, on the one hand we directly average the transverse magnetic susceptibility in real space over different disorder configurations and on the other hand we use the coherent potential approximation (CPA). While the method of direct averaging is numerically exact, it is computationally expensive and limited by the maximal size of the supercell which can be simulated on a computer. On the contrary the CPA does not suffer from this drawback and yields a cheap numerical scheme. Therefore, we additionally compare the results of these two approaches and show that the CPA gives very good results for most of the magnetic properties, including the magnon energies and the spatial shape of the eigenmodes. However, it turns out that while reproducing the general trend, the CPA systematically underestimates the disorder induced damping of the magnons. This provides evidence that the physics of impurity scattering in this system is governed by non-local effects missing in the CPA. Finally, we study the real space eigenmodes of the system, including their spatial shapes, and analyze their temperature dependence within the random phase approximation.